Refreshments at 9:30 AM
300 Ford Hall
While many statistical methods have been developed as tools of data analysis, statisticians constantly face the issue of choosing a suitable modelor method for accurate and reliable description of the nature of the data generating process or for prediction. Parametric model selection
criteria, such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), have been widely used for decades. Nonparametric
model/procedure evaluation methods (e.g. cross validation) are also intensively adopted. Rather than selecting a model/procedure from multiple
candidates, the approach of combining all candidates has received considerable attention in recent years. Empirical studies show that the
selection approach is often not reliable in model identification and a suitable combining method can significantly improve estimation and prediction.
This dissertation focuses on the adaptive combining method ARM (adaptive regression by mixing) for Gaussian regression and ACM method (adaptive classification by mixing) for pattern recognition. We show that the ARM method achieves an asymptotic optimality
under some conditions. Our simulation study shows ARM gives a combined estimator which is almost as good as the best estimator
among the candidates. We also investigate ARM weights on the models. For ACM, improved risk bounds are obtained in terms of the
squared L2 loss.